Not statistically significantly different... so what?


In a biomedical context, I would like to prove that my data are "similar" to other results (which I call "reference data").

All what I know from the reference data:
- mean: 79%
- sample size: 12

My own data:
- mean: 71%
- sample size: 6
- sd: 13.6

My data are not gaussian (bounded by 0 and 1). If I use a student t-test (I shouldn't... ^^), it shows that my data are not statistically significantly different from the reference data (p = 0.6)... so what? p<0.05 would have enabled me to conclude that it was different... but p>0.05 does not prove that they come from the same distribution or that they are "similar" in a certain way...

- I have read about the Lachin table wich could strengthen my conclusions of non statistical significant difference (I the power is high enough, it could prove that, if the two distributions would have been different, I would have detected it), is it the right way to go, especially given the small number of samples?
- If not, do you know any statistical test to assess if data are "similar" to others?

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